This invention generally relates to graphic display devices and more specifically to electronic circuits for generating control voltages, or vectors, for drawing straight lines between data points in a Cartesian coordinate system having a horizontal (X) axis and a vertical (Y) axis. The data points may be described in coordinate pairs, e.g., i x.sub.o, y.sub.o ; x.sub.1, y.sub.1 ; x.sub.2, y.sub.2 ; x.sub.3, y.sub.3 ; etc.
According to the rules of vector algebra, any vector R may be described by the sum of the vector components along the X and Y axis. The mathematical expression for a vector connecting a pair of data points 0 and 1, for example, is EQU R = (x.sub.1 - x.sub.o)i + (y.sub.1 - y.sub.o)j
Where i and j are vector symbols corresponding to the X and Y axis respectively, and the magnitude of R may be obtained from the expression EQU R = [(x.sub.1 - x.sub.o) + (y.sub.1 - y.sub.o)].sup.1/2
which is the familiar square root of the sum of the squares which is utilized to calculate the diagonal of a right triangle.
In the field of computer graphics, various vector generator schemes have been devised for increasing computer efficiency by reducing the writing time for a display image. Typically, the computer provides information defining the location of a series of data points, which when connected together form the image. One scheme for forming the mathematical representation of a vector is taught by U.S. Pat. No. 3,772,563 to Hasenbalg, in which straight lines are drawn between data points on a cathode-ray tube screen. In this patent, however, the vector drawing speed is not constant, but is an exponential function. Since line width and brightness may vary noticeably with the speed at which a vector is drawn, it is an important requirement that the "writing speed" of the writing element (e.g., electron beam in a cathode-ray tube device or ink pen in a X-Y plotter device) is constant over the entire length of the line.
A system for generating vectors of variable length and angle in which the writing speed is substantially constant, regardless of line length or angle, is described in U.S. Pat. No. 3,800,183 to Halio. In this particular system, two binary numbers identify the deflection components .DELTA.X and .DELTA.Y. The component having the greater magnitude is detected and utilized to set the slope of a ramp voltage which in turn energizes two digital-analog converter circuits in parallel. Each converter circuit produces an output which is a function of the product of the ramp voltage and a binary number corresponding to the .DELTA.X or .DELTA.Y component. The output signals, which when applied to the X and Y deflection circuitry, produce a vector which is drawn at a constant velocity. The circuitry which is required to produce these output signals is complex and requires many electrical components.